Question

Como faz o número 18 ????

Answer 1

Resposta:

a)

$log_{3}(18) + log_{3}(30) - log_{3}(4) - log_{3}(5) = \\ \\ log_{3}( \frac{18 \times 30}{4 \times 5} ) = \\ \\ log_{3}( \frac{18 \times 6}{4} ) = \\ \\ log_{3}( \frac{9 \times 6}{2} ) = \\ \\ log_{3}(9 \times 3) = \\ \\ log_{3}(27) = \\ \\ log_{3}(3^{3} ) = \\ \\ 3$

$2 \times log_{2}(6) + log_{2}(5) - log_{2}(3) - 2 \times log_{ {2}^{2} }(15) = \\ 2 \times log_{2}(6) + log_{2}(5) - log_{2}(3) - 2 \times \frac{1}{2} \times log_{2}(15) = \\ \\ 2 \times log_{2}(6) + log_{2}(5) - log_{2}(3) - log_{2}(15) = \\ log_{2}( {6}^{2} ) + log_{2}( \frac{5}{3 \times 15} ) = \\ \\ log_{2}(36) + log_{2}( \frac{1}{9} ) = \\ \\ log_{2}(36 \times \frac{1}{9} ) = \\ \\ log_{2}(4) = \\ \\ log_{2}( {2}^{2} ) = \\ \\ 2$